Doppler effect of gravity waves

Could the Doppler affect applied to gravity waves be seen as an explanation for mass?

I am a high school physics teacher with an interest in quantum physics but no mathematical background to understand highly technical replies. I thought of the above explanation for mass, and would like some feedback.

My logic is as follows: Inertial mass requires that a force applied over a distance (work) be applied to change the velocity of any mass. If an object with mass is accelerated, the frequency of its gravity waves should shift. Higher frequency gravity waves represent higher energy and the source of that energy could be considered to be the force applied over a distance (work) applied. So the reason it takes energy to accelerate a mass is because doing so increases the frequency of the mass' gravity waves. If this is true, perhaps we don't need particles (such as the Higgs boson) to explain mass.